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They're equivalent. 1 J is equal to 1 Newton*1 meter (N*m), and a Newton is equal to a kilogram times a meter per second squared (kg m/s2). Therefore, substituting kg m/s2 for the Newton, and multiplying it by a meter, a Joule is a kg m2/s2. If it's Joules per kg, then it's (kg m2/s2)/kg, and the kg unit on the top and the bottom cancel each other out. You're left with m2/s2!

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